Methods for codebook sub-sampling

ABSTRACT

Disclosed are methods for codebook sub-sampling. In various implementations, a wireless terminal receives a reference signal, determines, based on the reference signal, a first precoding index i 2  for a first subband and a second precoding index i′ 2  for a second subband. The wireless terminal transmits a representation of i 2  and a representation of  4  to a base station. In various implementations, i′ 2  belongs to the set S i     2    which, in one implementation, equals {mod(i 2 −K 1 k,K), k=0, 1, . . . , K 2 }, where K 1 &gt;1, and where K 2 &gt;1 and K&gt;1 are integers. According to an implementation, the wireless terminal receives the reference signal from a first base station and transmits the representations of i 2  and i′ 2  to a second base station.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of U.S. Non-Provisional patentapplication Ser. No. 15/235,429, filed Aug. 12, 2016, which is adivisional of U.S. Non-Provisional patent application Ser. No.14/292,987 (now U.S. Pat. No. 9,432,101), filed Jun. 2, 2014, andentitled METHODS FOR CODEBOOK SUB-SAMPLING, which claims priority toU.S. Provisional Patent Application No. 61/832,206, filed Jun. 7, 2013,and entitled METHOD FOR FEEDBACK COMPRESSION FOR SINGLE USER AND MULTIUSER MIMO OPERATION, the contents of which are incorporated herein byreference.

TECHNICAL FIELD

The present disclosure is directed to wireless communications and, moreparticularly, to methods of codebook sub-sampling.

BACKGROUND

A Multi-Input Multi-Output (“MIMO”) communication system uses aplurality of channels in a spatial area. Antenna arrays that havemultiple transmission antennas can increase the capacity of datatransmission through MIMO-transmission schemes.

In a MIMO-communication system, base stations and wireless terminals usecodebooks for precoding information streams prior to transmission. Eachcodebook contains a number of elements. Each element of a codebook is avector or a matrix, termed a precoding vector or a precoding matrix,respectively. To optimize communication with a base station, a wirelessterminal determines various characteristics of the communication channelbetween the base station and itself, selects what it determines to bethe best matrix or vector from a codebook, and indicates this selectionto the base station. The base station may (but is not required to) usethat matrix or vector for precoding data streams prior to transmissionto the wireless terminal.

To indicate to the base station which matrix or vector it has selected,the wireless terminal transmits one or more codebook indices to the basestation. A codebook index is an index of a precoding matrix. Forexample, given a first precoding matrix W₁ and a second precoding matrixW₂, W₁ can be at least partially represented by a first index i₁, and W₂can be at least partially represented by a second index i₂. Put anotherway, the first codebook index i₁ can be used to identify or point to anelement in a first codebook of a set of W₁ matrices. The second codebookindex i₂ can be used to identify or point to an element in a secondcodebook of a set of W₂ matrices. Together, i₁ and i₂ jointly determinea precoding matrix, W, with a product structure, i.e., W=W₁W₂.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

While the appended claims set forth the features of the presenttechniques with particularity, these techniques may be best understoodfrom the following detailed description taken in conjunction with theaccompanying drawings of which:

FIG. 1 is a block diagram of a communication system;

FIG. 2 is a block diagram of a representative wireless terminal or basestation;

FIG. 3 is a flowchart showing a method of codebook sub-sampling carriedout by a wireless terminal;

FIG. 4 is a flowchart showing another method of codebook sub-samplingcarried out by a wireless terminal; and

FIG. 5 is a flowchart showing yet another method of codebooksub-sampling carried out by a wireless terminal.

DETAILED DESCRIPTION

Turning to the drawings, wherein like reference numerals refer to likeelements, techniques of the present disclosure are illustrated as beingimplemented in a suitable environment. The following description isbased on embodiments of the claims and should not be taken as limitingthe claims with regard to alternative embodiments that are notexplicitly described herein.

The present disclosure describes methods for codebook sub-sampling. Invarious embodiments, a wireless terminal receives a reference signal,determines, based on the reference signal, a first precoding index i₂for a first subband and a second precoding index i′₂ for a secondsubband. The wireless terminal transmits a representation of i₂ and arepresentation of i′₂ to a base station. In various embodiments, i′₂belongs to the set S_(i) ₂ which, in one implementation, equals{mod(i₂−K₁+k,K), k=0, 1, . . . , K₂}, where K₁>1 and K₂>1 and K>1 areintegers. According to an embodiment, the wireless terminal receives thereference signal from a first base station and transmits therepresentations of i₂ and i′₂ to a second base station.

Turning to FIG. 1, a wireless terminal 100 according to an embodiment isconfigured to communicate wirelessly with both a first base station 102and a second base station 104 (either one at a time or in parallel). Thefirst base station 102 and the second base station 104 are two of manybase stations of a wireless network 106 and are connected to other partsof the wireless network 106 by one or more well known mechanisms.Possible implementations of the wireless network 106 include a cellularnetwork (such one that follows standards set by the Third GenerationPartnership Project (“3GPP”)) and an Institute of Electrical andElectronics Engineers 802.11x network. Possible implementations of thewireless terminal 100 include a wireless telephone, a cellulartelephone, a personal digital assistant, a pager, a personal computer, aselective call receiver, a tablet computer, a camera, an automotiveproduct, a household product, a television, and a radio. The wirelessterminal 100 is configured to carry out the various methods describedherein.

Possible implementations of the first base station 102 and the secondbase station 104 include a macro base station, remote radio read(“RRH”), relay node, pico base station, femto base station, networktransmission point, and network reception point. For example, the firstbase station 102 can be a macro base station, and the second basestation 104 can be RRH. Furthermore, the first base station 102 and thesecond base station 104 can be different logical or physical entities orthey can be the same.

FIG. 2 illustrates a device 200 that is a possible implementation of thewireless terminal 100, the first base station 102, or second basestation 104 of FIG. 1. The device 200 includes a user interface 208, acontroller 210, a memory 220 (which can be implemented as volatilememory or non-volatile memory), a first transceiver 240, a secondtransceiver 241, an input-output interface 250, a network interface 260,and one or more antennas 221 arranged as a MIMO array 223. Thecontroller 210 retrieves instructions from the memory 220 and operatesaccording to those instructions to provide outgoing data to and receiveincoming data from the first transceiver 240 and the second transceiver241. The controller 210 also receives data from and sends data toexternal devices via the input-output interface 250. If the device 200is a base station, then the network interface 260 is coupled to abackhaul network, and the controller 210 can transmit data to otherelements of the wireless network 106 (FIG. 1) via the backhaul network(not shown).

During operation, one or more of the transceivers 240 and 241 receivesdata from the controller 210 and transmits Radio Frequency (“RF”)signals representing the data via one or more of the antennas 221.Similarly, each transceiver receives RF signals via one or more of theantennas 221, converts the signals into the appropriately formatteddata, and provides the data to the controller 210.

Each of the elements of the device 200 is communicatively linked to theother elements via data pathways 270. Possible implementations of thedata pathways 270 include wires, conductive pathways on a microchip, andwireless connections. Possible implementations of the controller 210include a microprocessor, a microcontroller, and a computer. Possibleimplementations of the network interface 260 include a modem, a networkinterface card, and a wireless local area network chipset.

In an embodiment, the wireless terminal 100 transmits data and certaintypes of control information to a base station (e.g., the first basestation 102 or the second base station 104) on a physical uplink sharedchannel (“PUSCH”). The wireless terminal 100 transmits controlinformation to a base station on a physical uplink control channel(“PUCCH”). Data carried by the PUSCH includes user data such as videodata (e.g., streaming video) or audio data (e.g., voice calls).

In an embodiment, a base station of the wireless network 106 (such asthe first base station 102) transmits a channel-state informationreference signal (“CSI-RS”), which the wireless terminal 100 uses forthe purpose of determining the state of the channel. The wirelessterminal 100 feeds back information regarding the determined channelstate in the form of a channel-state information (“CSI”) report. EachCSI report includes one or more of a channel-quality indicator (“CQI”),a precoding-matrix indicator (“PMI”), a precoder-type indication(“PTI”), and a rank indicator (“RI”). The wireless terminal 100 uses thePMI to indicate, to the base station, a recommended precoder matrix forthe downlink transmissions, the RI to recommend the transmission rank(number of transmission layers) that is preferably to be used fordownlink transmission to the wireless terminal 100, and the PTI tosignal the contents and timing of future CSI reports. The RI and the PMImay be separately encoded (e.g., mapped to different sets of bits in amessage) or jointly encoded. The base station uses higher-layersignaling to indicate to the wireless terminal 100 things such as thesub-frame periodicity, sub-frame offset (relative to a radio frameboundary), and the number of CSI-RS antenna ports that are configurable.In some embodiments, the base station transmits a cell-specificreference signal, which the wireless terminal 100 can use for samepurposes it would otherwise use the CSI-RS.

In an embodiment, the PMI corresponds to the first index (i₁) or thesecond index (i₂). The PMI, and thus the first index (i₁) and the secondindex (i₂), is conditioned on the most recent RI. For example, thewireless terminal 100 may determine a third precoding index based on thereference signal. In this example, the third precoding index points to athird precoding matrix of a second codebook, and the third precodingmatrix commonly applies to the first subband and the second subband.

In an embodiment, the network 106 is a 3GPP network that uses a Release12 precoding scheme. In one implementation for a Release 12 precodingscheme for four transmit antenna ports and rank 1-2 (based on theproduct W₁W₂ structure), each PMI value corresponds to a pair ofcodebook indices (i₁, i₂). In an embodiment, the channel qualityinformation represented by the CQI refers to one or more spatial layersand is conditioned on the precoding indices i₁ and i₂. Oneimplementation of these codebook indices is given in Table 1 for 1-layerCSI reporting using antenna ports 0 to 3 or 15 to 18, and given in Table2 for 2-layer CSI reporting using antenna ports 0 to 3 or 15 to 18,where ϕ_(n)=e^(jπn/2), θ_(r)=e^(jπr/16), and ν_(m)=[1 e^(j2πm/32)]^(T).

TABLE 1 i₂ i₁ 0 1 2 3 4 5 6 7 0-15 W_(i) ₁ _(,0,0) ⁽¹⁾ W_(i) ₁ _(,1,0)⁽¹⁾ W_(i) ₁ _(,2,0) ⁽¹⁾ W_(i) ₁ _(,3,0) ⁽¹⁾ W_(i) ₁ _(+8,0,1) ⁽¹⁾ W_(i)₁ _(+8,1,1) ⁽¹⁾ W_(i) ₁ _(+8,2,1) ⁽¹⁾ W_(i) ₁ _(+8,3,1) ⁽¹⁾ i₂ i₁ 8 9 1011 12 13 14 15 0-15 W_(i) ₁ _(+16,0,2) ⁽¹⁾ W_(i) ₁ _(+16,1,2) ⁽¹⁾ W_(i)₁ _(+16,2,2) ⁽¹⁾ W_(i) ₁ _(+16,3,2) ⁽¹⁾ W_(i) ₁ _(+24,0,3) ⁽¹⁾ W_(i) ₁_(+24,1,3) ⁽¹⁾ W_(i) ₁ _(+24,2,3) ⁽¹⁾ W_(i) ₁ _(+24,3,3) ⁽¹⁾${{where}\mspace{14mu} W_{m,n,r}^{(1)}} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\phi_{n}\theta_{r}v_{m}}\end{bmatrix}}$

TABLE 2 i₂ i₁ 0 1 2 3 4 5 6 7 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁_(,i) ₁ _(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁ _(+16,1)⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1) ⁽²⁾ i₂i₁ 8 9 10 11 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i)₁ _(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁ _(+24,1) ⁽²⁾ W_(i) ₁_(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1) ⁽²⁾${{where}\mspace{14mu} W_{m,{m'},n}^{(2)}} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m'} \\{\phi_{n}v_{m}} & {{- \phi_{n}}v_{m'}}\end{bmatrix}}$

For 4 antenna ports {0, 1, 2, 3} or {15, 16, 17, 18}, a first PMI valueof n₁ ∈{0, 1, . . . , f(υ)−1} and a second PMI value of n₂ ∈{0, 1, . . ., g(υ)−1} correspond to the codebook indices n₁ and n₂ given in Table 1for υ, the associated RI value, equal to one and Table 2 for υ equal totwo, f(υ)=16, υ∈{1, 2}, and g(υ)=16, υ∈{1, 2}.

In an embodiment, the W₂ matrices of a codebook are ordered based ondistinct beam groups and then ordered using intra-group ordering basedon different co-phasing assumptions. One implementation of this orderingfor i₂ is shown in the codebooks in Table 1 and Table 2, in which theprecoding matrices within a beam group (defined by the vector ν_(m) (forrank 1) and the pair of vectors (ν_(m), ν_(m′)) (for rank 2)) differ inonly the co-phasing terms defined by quantities ϕ_(n) and θ_(r). Forexample, assume the selected index is i₂ n_(k-1)=5 (indexed startingfrom 0) for subband k−1. The wireless terminal 100 can select the W₂index n_(k) for subband k from the range [n_(k-1)−3, n_(k-1)+4](ignoring edge conditions). More generally, for any index i₂ for subbandm, the wireless terminal 100 selects index i₂ for subband n from the setof indices {mod(i₂−3+k, 16), k=0, 1, . . . , 7}. In an embodiment, n isnot equal tom (e.g., n=m+1 or n=m−1). The wireless terminal 100 can thenencode the resulting selection using 3 bits. The 3-bit differentialcodebook index i₂′ for subband n can be i₂′ (n)=k. Thus, the codebookindex i₂ for subband n can then be given as i₂(n)=mod(i₂ (n−1)−3+i₂′(n),16). As a result, for any W₂ feedback i₂ (k−1) that the wirelessterminal 100 selects for subband k−1, the wireless terminal 100 selectsfrom the i₂ indexes in the set of {mod(i₂ (k−1)−3+q, 16), q=0, 1, . . ., 7} for i₂ feedback in subband k. This limit on the possible selectionof i₂ means that, while the first subband (i.e., the subband with thelowest frequency index) requires 4 bits for i₂, the remainder of thesubbands require only 3 bits for i₂ (3 bits i′₂′ for the differentialrepresentation).

In another embodiment, the wireless terminal 100 determines adifferential PMI starting out from the center subband (a subband at thecenter or close to the center of the set of subbands or the systembandwidth with full 4-bits codebook index i₂ representation) proceedingin both directions. In still another embodiment, the wireless terminal100 determines a full 4-bit feedback representation of codebook index i₂for a subset of the subbands and a 3-bit differential representation i′₂of codebook index i₂ for the remaining subbands. For example, the subsetof the subbands for full 4-bit feedback representation of codebook indexi₂ may be the {first subband, center subband} or {first subband, centersubband, last subband}.

Consider the following rank-1 codebook solution (“Solution 1”):

$\mspace{20mu} {{W_{1} = {{\begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}\mspace{14mu} {where}\mspace{14mu} n} = 0}},1,\ldots \mspace{14mu},15}$$\mspace{20mu} {X_{n} = {{\begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}\mspace{14mu} {where}\mspace{14mu} q_{1}} = e^{j\; 2{\pi/32}}}}$$\mspace{20mu} {{{For}\mspace{14mu} {rank}\mspace{14mu} 1},{W_{2,n} \in \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{\alpha (i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\; {\alpha (i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- {\alpha (i)}}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\; {\alpha (i)}Y}\end{bmatrix}}} \right\}}}$  and  Y ∈ {e₁, e₂, e₃, e₄}  and  α(i) = q₁^(2(i − 1));$\mspace{20mu} {{{For}\mspace{14mu} {rank}\mspace{14mu} 2},\mspace{20mu} {W_{2,n} \in \left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}}$  and(Y₁, Y₂) = (e_(i), e_(k)) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)}.

Additionally, consider the following rank-1 codebook solution (“Solution2”):

$\mspace{20mu} {{W_{1} = {{\begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}\mspace{14mu} {where}\mspace{14mu} n} = 0}},1,\ldots \mspace{14mu},15}$$\mspace{20mu} {X_{n} = {{\begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}\mspace{14mu} {where}\mspace{14mu} q_{1}} = e^{j\; 2{\pi/32}}}}$$\mspace{20mu} {{{For}\mspace{14mu} {rank}\mspace{14mu} 1},{W_{2,n} \in \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{\alpha (i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{j\; {\alpha (i)}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- {\alpha (i)}}Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{{- j}\; {\alpha (i)}Y}\end{bmatrix}}} \right\}}}$  and  Y ∈ {e₁, e₂, e₃, e₄}  and  α(i) = q₁^(2(i − 1));$\mspace{20mu} {{{For}\mspace{14mu} {rank}\mspace{14mu} 2},{W_{2,n} \in {\left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\} \left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}}}$  and $W_{2,n} \in {\left\{ {{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\} \left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$  and $W_{2,n} \in {\left\{ {\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}} \right\} \left( {Y_{1},Y_{2}} \right)} \in {\left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}.}$

Under both Solution 1 and Solution 2, the W₂ vector can be written as:

${W_{2} = {\frac{1}{\sqrt{2}}\begin{bmatrix}e_{i} \\{\beta_{2}{\alpha (i)}e_{i}}\end{bmatrix}}},$

where α(i)=exp(j2π·2 (i−1)/32), i=1, 2, 3, 4, and β₂ ∈{1, −1, j, −j}.The index i determines the beam group while β₂ determines the co-phasingterms in the equation above. With respect to the codebook embodiments ofTable 1 and Table 2, where the terms ϕ_(n)=e^(jπn/2), θ_(r)=e^(jπr/16),and ν_(m)=[1 e^(j2πm/32)]^(T) were defined, the index m, whichdetermines ν_(m), equivalently identifies the beam group, and indices nand r, which determine ϕ_(n) and θ_(r), identify the co-phasing terms.Therefore, ordering the W₂ codewords first based on beam groups and thenon co-phasing terms, according to an embodiment, leads to the orderingfor the W₂ codebook shown in Table 3 and the product W₁W₂ codebook shownin Table 4.

TABLE 3 i₂ i₁ 0 1 2 3 4 5 6 7 0-15 W_(1,0) ⁽²⁾ W_(1,1) ⁽²⁾ W_(1,2) ⁽²⁾W_(1,3) ⁽²⁾ W_(2,0) ⁽²⁾ W_(2,1) ⁽²⁾ W_(2,2) ⁽²⁾ W_(2,3) ⁽²⁾ i₂ i₁ 8 9 1011 12 13 14 15 0-15 W_(3,0) ⁽²⁾ W_(3,1) ⁽²⁾ W_(3,2) ⁽²⁾ W_(3,3) ⁽²⁾W_(4,0) ⁽²⁾ W_(4,1) ⁽²⁾ W_(4,2) ⁽²⁾ W_(4,3) ⁽²⁾${{{where}\mspace{14mu} W_{i,k}^{(2)}} = {\frac{1}{2}\begin{bmatrix}e_{i} \\{\beta_{k}{\alpha (i)}e_{i}}\end{bmatrix}}},{{\alpha (i)} = {\exp \left( {j\; 2\; {\pi \cdot 2}{\left( {i - 1} \right)/32}} \right)}},\; {\beta_{k} = {\exp \; \left( {j\; 2\; \pi \; {k/4}} \right)}}$

TABLE 4 i₂ i₁ 0 1 2 3 4 5 6 7 0-15 W_(i) ₁ _(,0,0) ⁽¹⁾ W_(i) ₁ _(,1,0)⁽¹⁾ W_(i) ₁ _(,2,0) ⁽¹⁾ W_(i) ₁ _(,3,0) ⁽¹⁾ W_(i) ₁ _(+8,0,1) ⁽¹⁾ W_(i)₁ _(+8,1,1) ⁽¹⁾ W_(i) ₁ _(+8,2,1) ⁽¹⁾ W_(i) ₁ _(+8,3,1) ⁽¹⁾ i₂ i₁ 8 9 1011 12 13 14 15 0-15 W_(i) ₁ _(+16,0,2) ⁽¹⁾ W_(i) ₁ _(+16,1,2) ⁽¹⁾ W_(i)₁ _(+16,2,2) ⁽¹⁾ W_(i) ₁ _(+16,3,2) ⁽¹⁾ W_(i) ₁ _(+24,0,3) ⁽¹⁾ W_(i) ₁_(+24,1,3) ⁽¹⁾ W_(i) ₁ _(+24,2,3) ⁽¹⁾ W_(i) ₁ _(+24,3,3) ⁽¹⁾${{where}\mspace{14mu} W_{m,n,r}^{(1)}} = {{{\frac{1}{2}\begin{bmatrix}v_{m} \\{\beta_{n}{\alpha (r)}v_{m}}\end{bmatrix}}\mspace{25mu} \beta_{n}} = {{e^{{j\; 2\; \pi}\;}\mspace{20mu} {\alpha (r)}} = e^{j\; 2{\pi \; \cdot 2}{r/32}}}}$

Ordering the W₂ codebook in the manner shown in Table 3 ensures thatvectors within the same beam group (i.e., i index) are assigned toconsecutive indices. With 3 bits for i₂, all of the precoding vectorswithin the same beam group are included in the reduced precoding vectorset.

To generalize, the wireless terminal 100 can determine a secondprecoding index i₂ based on the reference signal. The second precodingindex i₂ is an index of a second codebook W₂. The first precoding indexi₁ and second precoding index i₂ jointly determine a precoding matrix ofa third codebook W₁W₂, which has a product structure.

It should be noted that the rank-2 W₂ matrix for Solution 2 includes adiverse set of structures for beam selection and co-phasing. On theother hand, the rank-2 W₂ matrix for Solution 1 is more regular, in thatthere are only two co-phasing structures and 8 beam pairs. Therefore, insome embodiments, the two-stage ordering (first based on beam groups andnext on co-phasing terms) may work better for Solution 1, rank 2, thanfor Solution 2, rank 2.

As an alternative, consider a subspace distance between two W₂ matrices,P₁ and P₂ defined as:

d(P ₁ ,P ₂)½∥P ₁ P ₁ ^(H) −P ₂ P ₂ ^(H)∥_(F),

where ∥·∥_(F) denotes the Frobenius norm, and where the subspacedistance determines the distance between the subspace spanned thecolumns of P₁ and P₂.

According to an embodiment, Table 5 tabulates the seven nearest W₂matrices for each W₂ matrix with respect to subspace distance. The W₂candidates of Table 5 are ordered with increasing subspace distance foreach index i₂ for Solution 2, rank 2. In the case of a large number ofties (e.g., i₂=4, 5), the codewords in the corresponding row areselected randomly. Otherwise for most other rows, it is observed thatthere are only a few ties.

TABLE 5 Index Candidates for i2′ are {i2} U {k_i(i2)} i2 k_1(i2) k_2(i2)k_3(i2) k_4(i2) k_5(i2) k_6(i2) k_7(i2) 0 1 8 9 12 13 11 15 1 2 8 9 1213 11 15 2 3 8 9 10 11 14 15 3 2 8 9 10 11 14 15 4 5 10 11 9 13 15 0 5 410 11 9 13 15 0 6 7 12 13 14 15 9 11 7 6 12 13 14 15 9 11 8 0 1 2 3 9 1211 9 0 1 2 3 8 13 10 10 2 3 4 5 11 14 9 11 2 3 4 5 10 15 8 12 0 1 6 7 813 14 13 0 1 6 7 9 12 15 14 2 3 6 7 10 12 15 15 2 3 6 7 11 13 14

In one embodiment, the wireless terminal 100 takes the subspace distanceas the ranking metric into account as follows. The wireless terminal 100selects index i₂ (m−1) for subband (m−1). For subband m, the only set ofcandidates the wireless terminal 100 evaluates for selection is given bythe set S_(i) ₂ ={i₂ (m−1)}∪A_(i) ₂ , where

$A_{i_{2}} = {\underset{i = 1}{\bigcup\limits^{7}}\left\{ {k_{i}\left( i_{2} \right)} \right\}}$

and k_(i) (i₂), i₂=0, 1, . . . , 15 as shown in Table 5. In other words,i′₂ belongs to a subset of the first codebook and includes the firstprecoding index i₂.

The W₁(n)=diag {X_(n), X_(n)} structure that is common to Solution 1 andSolution 2 has the component matrix:

$X_{n} = {\begin{bmatrix}1 & 1 & 1 & 1 \\q^{n} & q^{n + 8} & q^{n + 16} & q^{n + 24}\end{bmatrix}.}$

W₁ (n) and W₁ (n+8) have the same columns except for a cyclic shift(i.e., the columns of W₁(n+8) are cyclically left-shifted version of thecolumns of W₁(n) for 0≤n≤7).

For rank 1, W₂ includes a beam-selection component matrix Y that canchoose any beam for antenna port pairs (#15, #16) and (#17, #18) butwith a phase offset for one co-polarized pair with respect to the other.The beam-space matrix W (n) can be compressed to 3 bits (e.g., PUCCH 1-1submode 1 and submode 2) for rank 1 (i.e., if the last reported RI is 1)with a potential degradation in performance. This suggests asub-sampling of the form I_(PMI)=mod(i₁, 8), where I_(PMI) representsthe sub-sampled PMI and i₁∈{0, 1, . . . , 15} is the PMI index for W₁.In other words, for rank 1, from the value of the first PMI, I_(PMI1)∈{0, 1, . . . , 7}, the codebook index i₁ is determined as i₁=I_(PMI1).

For rank 2, however, due to the restrictions on W₂, W₁(n) and W₁(n+8)different overall codebooks (W₁W₂) result for both Solution 1 andSolution 2 when W₂ takes on different values. For solution 1, theallowed pairs of columns of X_(n) that can be selected for (Y₁, Y₂) are(1,1), (2,2), (3,3), (4,4), (1,2), (2,3), (1,4), (2,4). The allowedpairs of columns of X_(n+8) (using the column indexes of X_(n)) aretherefore (1,1), (2,2), (3,3), (4,4), (2,3), (3,4), (2,1), (3,1). Onepair (1,2) has swapped Y₁ and Y₂, and two other pairs (1,4) and (2,4)are replaced with different pairs (3,4) and (3,1). The remaining 5 pairsare common. However, there are different co-phasings of Y₁ and Y₂ thatlead to some common beams for different (mod(i₁, 8), i₂) and (mod(i₁,8)+8, i₂) combinations. If the sub-sampling I_(PMI)=mod(i₁, 8) isadopted, then for W₁(n) and W₁(n+8), all of the 32 columns (for each oflayer 1 and layer 2) occurring in the precoder set generated using W₁(n)appear as columns in the precoder set generated using W₁(n+8).Furthermore, 10 of the 16 rank-2 product W₁W₂ matrices appear commonlyin the precoder sets generated using W₁(n) and W₁(n+8).

In some embodiments, the sub-sampling described above can result in aperformance loss for rank 2. Thus, for both Solution 1 and Solution 2,if compression is not desired (e.g., in PUSCH 3-2), then 3 bits can beused for W₁ feedback under rank 1, and 4 bits can used for W₂ feedbackunder rank 2.

It is possible that the degradation due to sub-sampling is smaller forrank 1 than it is for rank 2. Accordingly, in an embodiment, thewireless terminal 100 determines the precoding index i₁ based on thereference signal received from the first base station 102, where i₁ isan index pointing to a first codebook, and where the elements of thecodebook can be represented by K=4 bits. If the preferred transmissionrank is 1 or if the last reported RI corresponds to rank 1, then thewireless terminal 100 can transmit a report that includes an M=3 (<K)bit representation of i₁ to the second base station 104 (or some other Msuch that M is different from K). Alternatively, if the preferredtransmission rank is 2 or if the last reported RI corresponds to rank 2,then the wireless terminal 100 can transmit a K=4 bit representation ofi₁ to the second base station 104.

In an embodiment, for PUCCH 1-1, submode 1, when sub-sampling isdesired, the wireless terminal 100 uses 3 bits for the first PMI byreporting I_(PMI)=mod(i₁, 8) with 1 bit for RI (for rank 1/2) and 2-bitRI (for rank 3/4). For PUCCH 1-1 submode 2, 3 bits can be used for thefirst PMI by reporting I_(PMI)=mod(i₁,8). The wireless terminal 100 mayneed to carry out compression for the second PMI (W₂) for rank 2 toensure that the payload size is 11 bits. For PUCCH 2-1, the wirelessterminal 100 may need to carry out compression for a second PMI as well.For PUCCH 1-1 submode 2 and PUCCH 2-1, where the wireless terminal 100may need to carry out compression for the second PMI, a simpleco-phasing structure for W₂ such as:

${W_{2} = {\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}}$

for rank 1 and:

${W_{2} = {\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}}},{\frac{1}{2}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}$

for rank 2 (which is the common co-phasing structure for both Solution 1and Solution 2) may be appropriate. In one embodiment, the vectors Y,Y₁, and Y₂ can be set equal to e₁ which selects the first and fifthcolumn of W₁.

Turning to FIG. 3, a flowchart 300 illustrates an embodiment of thedisclosure. At step 302, the wireless terminal 100 receives a referencesignal (e.g., from the first base station 102). At step 304, thewireless terminal 100 determines, based on the reference signal, a firstprecoding index i₂ for a first subband. i₂ is an index of a firstcodebook. At step 306, the wireless terminal 100 determines, based onthe reference signal, a second precoding index i′₂ for a second subband.In an embodiment, i′₂ is an index for the first codebook and belongs tothe set {mod(i₂−K₁+k,K), k=0, 1, . . . , K₂}, where K₁>1, and K₂>1 andK>1 are integers. In one implementation, K₁<K₂<K (e.g., K₁=3, K₂=7, andK=16). At step 308, the wireless terminal 100 transmits a representationof i₂ and a representation of i′₂ to a base station (e.g., the basesecond station 104).

Turning to FIG. 4, a flowchart 400 illustrates an embodiment of thedisclosure. At step 402, the wireless terminal 100 receives a referencesignal from the first base station 102. At step 404, the wirelessterminal 100 determines a first precoding index i₁ based on thereference signal, wherein i₁ points to an element of a first codebook.At step 406, the wireless terminal 100 determines a derived precodingindex I_(PMI)=mod(i₁,K), wherein K>1 is an integer. At step 408, thewireless terminal 100 transmits a representation of I_(PMI) to thesecond base station 104.

Turning to FIG. 5, a flowchart 500 illustrates an embodiment of thedisclosure. At step 502, the wireless terminal 100 receives a referencesignal from the first base station 102. At step 504, the wirelessterminal 100 determines a first precoding index i₁ based on thereference signal. The first precoding index i₁ is an index of a firstcodebook. Elements of the first codebook can be represented by K bits.If, at step 506, the last reported RI corresponds to rank 1, then, atstep 508, then the wireless terminal 100 transmits, to the second basestation 104, a report that includes an M-bit representation of i₁. If,at step 506, the last reported RI corresponds to rank 2, then thewireless terminal 100 transmits, to the second base station 104, areport that includes a K-bit representation of i₁, wherein M<K at step510.

In some embodiments, the wireless terminal 100 carries out periodic CSIreporting. For example, the wireless terminal 100 may have two reportinginstances (a first and a second reporting instance) each with its ownperiodicity (a first periodicity and a second periodicity). The firstreporting instance is in a first uplink subframe, and the secondreporting instance is in a second uplink subframe. The first uplinksubframe and the second uplink subframe can occur at different times.The first and second periodicities may be different from one another.Thus, for example, the wireless terminal 100 can send a representationof a precoding index in a first CSI report on a first uplink subframeand send a representation of another precoding index in a second CSIreport on a second uplink subframe (e.g., i₂ in a first CSI report andi′₂ in a second CSI report, or i₁ in a first CSI report and i₂ in asecond CSI report). The first and second uplink subframes can beidentical. Likewise, the first and second CSI reports can be identical.

In one example, the wireless terminal 100 carries out wideband CQI andwideband PMI periodic reporting. In one mode of operation, the wirelessterminal 100 transmits a first CSI report on a first reporting instancewith the first periodicity. The first CSI report includes an RI and afirst PMI. The first PMI is a representation of the first index (i₁) Thewireless terminal 100 may transmit a second CSI report on the secondreporting instance with the second periodicity. The second CSI reportincludes the wideband CQI and the second PMI. The second PMI is arepresentation of the second index (i₂).

In another mode of operation, the wireless terminal 100 may transmit afirst CSI report including RI on the first reporting instances with thefirst periodicity. The wireless terminal 100 may transmit a second CSIreport including the wideband CQI and PMI, the PMI being arepresentation of the first index (i₁) and the second index (i₂) on thesecond reporting instances with the second periodicity.

In another embodiment, the wireless terminal 100 carries out subband CQIand PMI periodic reporting. In doing so, the wireless terminal 100determines a PTI and transmits a first CSI report including an RI andthe PTI on the first reporting instance with the first periodicity. Thewireless terminal 100 uses the PTI to indicate the contents of the CSIreports on the second reporting instances with the second periodicityuntil the next CSI report containing the RI and the PTI. If the mostrecently transmitted PTI is set to 0, then the wireless terminal 100transmits a second CSI report on a subset of the second reportinginstances with a third periodicity (e.g., third periodicity=k*secondperiodicity, k being an integer). If the most recently transmitted PTIis set to 0, then the second CSI report includes a first PMI, the firstPMI being a representation of the first index (i₁). Between every twoconsecutive first and second PMI reports on the second reportinginstances (with the second periodicity), the wireless terminal 100transmits a third CSI report, which includes a wideband CQI and a secondPMI that assumes transmission on a wideband channel bandwidth, thesecond PMI being a representation of the second index (i₂). In the caseof a CSI report collision (due to the wireless terminal 100 beingconfigured with multiple carriers (carrier aggregation) or multipleserving cells), the wireless terminal 100 transmits a CSI report of onlyone serving cell with the CSI report including only the representationof the first index (i₁) with a higher priority than other CSI reports.

If the most recently transmitted PTI is set to 1, then the wirelessterminal 100 transmits the second CSI report on a subset of the secondreporting instances with a fourth periodicity (e.g., fourthperiodicity=m*second periodicity, m being an integer), the second CSIreport including the wideband CQI and the third PMI, the third PMI beinga representation of the second index (i₂) that assumes transmission on awideband channel bandwidth. The fourth periodicity can be different fromthe third periodicity. Between every two consecutive wideband CQI andwideband second PMI reports on the second reporting instances with thesecond periodicity, the wireless terminal 100 transmits a fourth CSIreport including a subband CQI and a fourth PMI assuming transmission ona subband channel bandwidth, the fourth PMI being a representation ofthe second index (i₂).

In another embodiment, if the most recently transmitted PTI is set to 0,then the wireless terminal 100 transmits a second CSI report on a subsetof the second reporting instances with a third periodicity (e.g., thirdperiodicity=k*second periodicity, k being an integer). The second CSIreport includes a first PMI, the first PMI being a representation of thefirst index (i₁). Between every two consecutive first and second PMIreports on the second reporting instances with the second periodicity,the wireless terminal 100 transmits a third CSI report including awideband CQI and a second PMI that assumes transmission on a widebandchannel bandwidth, the second PMI being a representation of the secondindex (i₂). If the most recently transmitted PTI is set to 1, then thebehavior of the wireless terminal 100 is the same as described in theprevious mode of the operation above.

In view of the many possible embodiments to which the principles of thepresent discussion may be applied, it should be recognized that theembodiments described herein with respect to the drawing figures aremeant to be illustrative only and should not be taken as limiting thescope of the claims. Therefore, the techniques as described hereincontemplate all such embodiments as may come within the scope of thefollowing claims and equivalents thereof.

We claim:
 1. A method in a wireless terminal, the method comprising:receiving a reference signal from a first base station; determining afirst precoding index i₁ based on the reference signal, wherein i₁ is anindex of a first codebook; if a last reported Rank Indicator (RI)corresponds to rank 1, then transmitting, to a second base station, areport that includes an M bit representation of i₁; and if the lastreported RI corresponds to rank 2, then transmitting, to the second basestation, a report that includes a K-bit representation of i₁, whereinM<K.
 2. The method of claim 1, further comprising: determining a secondprecoding index i₂ based on the reference signal, wherein the secondprecoding index i₂ is an index of a second codebook, and wherein thefirst precoding index and second precoding index jointly determine aprecoding matrix of a third codebook with a product structure.
 3. Themethod of claim 2, wherein the third codebook comprises: i₂ i₁ 0 1 2 3 45 6 7 0-15 W_(i) ₁ _(,0,0) ⁽¹⁾ W_(i) ₁ _(,1,0) ⁽¹⁾ W_(i) ₁ _(,2,0) ⁽¹⁾W_(i) ₁ _(,3,0) ⁽¹⁾ W_(i) ₁ _(+8,0,1) ⁽¹⁾ W_(i) ₁ _(+8,1,1) ⁽¹⁾ W_(i) ₁_(+8,2,1) ⁽¹⁾ W_(i) ₁ _(+8,3,1) ⁽¹⁾ i₂ i₁ 8 9 10 11 12 13 14 15 0-15W_(i) ₁ _(+16,0,2) ⁽¹⁾ W_(i) ₁ _(+16,1,2) ⁽¹⁾ W_(i) ₁ _(+16,2,2) ⁽¹⁾W_(i) ₁ _(+16,3,2) ⁽¹⁾ W_(i) ₁ _(+24,0,3) ⁽¹⁾ W_(i) ₁ _(+24,1,3) ⁽¹⁾W_(i) ₁ _(+24,2,3) ⁽¹⁾ W_(i) ₁ _(+24,3,3) ⁽¹⁾${{where}\mspace{14mu} W_{m,n,r}^{(1)}} = {{{\frac{1}{2}\begin{bmatrix}v_{m} \\{\beta_{n}{\alpha (r)}v_{m}}\end{bmatrix}}\mspace{14mu} \beta_{n}} = {{e^{j\; 2\pi \; {n/4}}\mspace{20mu} {\alpha (r)}} = e^{j\; 2{\pi \cdot 2}\; {r/32}}}}$


4. The method of claim 2, further comprising: transmitting, to thesecond base station, a first report with a first periodicity, the firstreport including an RI; and transmitting, to the second base station, asecond report with a second periodicity, the second report including arepresentation of i₁ and i₂.
 5. The method of claim 2, furthercomprising: transmitting, to the second base station, a first reportwith a first periodicity, the first report including an RI and arepresentation i₁; and transmitting, to the second base station, asecond report with a second periodicity, the second report including arepresentation of i₂.
 6. The method of claim 2, further comprising:transmitting, to the second base station, a first report with a firstperiodicity, the first report including an RI and a precoder-typeindication (PTI); if a most recently transmitted PTI is set to 0, thentransmitting, to the second base station, a second report with aperiodicity based on a second periodicity, the second report including arepresentation of i₁; and if the most recently transmitted PTI is set to1, then transmitting, to the second base station, a second report withanother periodicity based on the second periodicity, the second reportincluding a representation of i₂.
 7. A wireless terminal comprising: atleast one transceiver operative to receive a reference signal from afirst base station; and a controller, operatively coupled to the atleast one transceiver operative to: determine a first precoding index i₁based on the reference signal, wherein i₁ is an index of a firstcodebook; if a last reported Rank Indicator (RI) corresponds to rank 1,then transmitting, to a second base station, a report that includes an Mbit representation of i₁; and if the last reported RI corresponds torank 2, then causing at least one transceiver to transmit, to the secondbase station, a report that includes a K-bit representation of i₁,wherein M<K.
 8. The wireless terminal of claim 7, wherein the controllerfurther operates to: determine a second precoding index i₂ based on thereference signal, wherein the second precoding index i₂ is an index of asecond codebook, and wherein the first precoding index and secondprecoding index jointly determine a precoding matrix of a third codebookwith a product structure.
 9. The wireless terminal of claim 8, whereinthe third codebook comprises: i₂ i₁ 0 1 2 3 4 5 6 7 0-15 W_(i) ₁ _(,0,0)⁽¹⁾ W_(i) ₁ _(,1,0) ⁽¹⁾ W_(i) ₁ _(,2,0) ⁽¹⁾ W_(i) ₁ _(,3,0) ⁽¹⁾ W_(i) ₁_(+8,0,1) ⁽¹⁾ W_(i) ₁ _(+8,1,1) ⁽¹⁾ W_(i) ₁ _(+8,2,1) ⁽¹⁾ W_(i) ₁_(+8,3,1) ⁽¹⁾ i₂ i₁ 8 9 10 11 12 13 14 15 0-15 W_(i) ₁ _(+16,0,2) ⁽¹⁾W_(i) ₁ _(+16,1,2) ⁽¹⁾ W_(i) ₁ _(+16,2,2) ⁽¹⁾ W_(i) ₁ _(+16,3,2) ⁽¹⁾W_(i) ₁ _(+24,0,3) ⁽¹⁾ W_(i) ₁ _(+24,1,3) ⁽¹⁾ W_(i) ₁ _(+24,2,3) ⁽¹⁾W_(i) ₁ _(+24,3,3) ⁽¹⁾${{where}\mspace{14mu} W_{m,n,r}^{(1)}} = {{{\frac{1}{2}\begin{bmatrix}v_{m} \\{\beta_{n}{\alpha (r)}v_{m}}\end{bmatrix}}\mspace{14mu} \beta_{n}} = {{e^{j\; 2\pi \; {n/4}}\mspace{20mu} {\alpha (r)}} = e^{j\; 2{\pi \cdot 2}\; {r/32}}}}$


10. The wireless terminal of claim 8, wherein the controller furtheroperates to: transmit, to the second base station, a first report with afirst periodicity, the first report including an RI; and transmit, tothe second base station, a second report with a second periodicity, thesecond report including a representation of i₁ and i₂.
 11. The wirelessterminal of claim 8, wherein the controller further operates to:transmit, to the second base station, a first report with a firstperiodicity, the first report including an RI and a representation i₁;and transmit, to the second base station, a second report with a secondperiodicity, the second report including a representation of i₂.
 12. Thewireless terminal of claim 8, wherein the controller further operatesto: transmit, to the second base station, a first report with a firstperiodicity, the first report including an RI and a precoder-typeindication (PTI); if a most recently transmitted PTI is set to 0, thentransmit, to the second base station, a second report with a periodicitybased on a second periodicity, the second report including arepresentation of i₁; and if the most recently transmitted PTI is set to1, then transmit, to the second base station, a second report withanother periodicity based on the second periodicity, the second reportincluding a representation of i₂.